Concept explainers
The He+ ion contains only one electron and is therefore a hydrogenlike ion. Calculate the wavelengths, in increasing order, of the first four transitions in the Balmer series of the He+ ion. Compare these wavelengths with the same transitions in a H atom. Comment on the differences. (The Rydberg constant for He+ is 8.72 × 10−18 J.)
Interpretation:
The wavelengths in the increasing order of the first four transitions in the Balmer series of the
Concept Introduction:
Absorption refers to how much light can be taken in by the material being measured.
Emission spectrum:
When electromagnetic radiation interacts with matter, atoms and molecules may absorb energy and reach to a higher energy state. With higher energy, these are in an unstable state. For returning to their normal (more stable, lower energy) energy state, the atoms and molecules emit radiations in various regions of the electromagnetic spectrum. The spectrum of radiation emitted by a substance that has absorbed energy is called an emission spectrum.
In 1885, Johann Balmer developed a simple equation which could be used to calculate the wavelengths of the four visible lines in the emission spectrum of hydrogen. Johannes Rydberg developed Balmer’s equation further, giving an equation which could calculate the visible wavelengths and also those of all hydrogen’s spectral lines.
This equation is known as the Rydberg equation. Here,
Answer to Problem 7.112QP
The wavelengths of the first four transitions in the Balmer series of the
Explanation of Solution
When one of helium’s electrons is removed, the resulting species is the helium ion,
Here, the Rydberg constant for
For the transition
The negative sign indicates that the emission of light occurs. Wavelengths are always positive signs. Here,
For the transition
For the transition
For the transition
The Rydberg constant for
The negative sign indicates that the emission of light occurs. Wavelengths are always positive signs. Here,
For the transition
For the transition
For the transition
All the Balmer transitions for
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